On flatter roads the 5.7 can pull the listed 8k+/- (max) with no problems, even with the 3.21. The long grades y'all see out west will be a different story...
Max cargo weight is 1600# +/-, tongue weight is a part of that figure. So if you get a TT near the max weight of 8K, you can expect 1100-1200# of tongue weight - leaving little for cargo. And fuel/people are included in the cargo figure.
And none of that covers handling/braking - these trucks are "rate" to tow 8-10k - but IMHO, they are not good at it at all. Braking, handling, soft rear end... (I tried towing 8.5K with my old 1500 and hated every min of it). So you will need air bags, helper springs, timbrens...
And, these trucks come with passenger rated "P" tires. They are not load rated, and in no way match the tow ratings of the vehicle - so you will need to upgrade to LT tires.
When looking at the TT weights, assume you will be at the max weight of the trailer, not the dry weight. The dry weight is the TT with no extras at all, no propane, gear, supplies, water, food - sometimes they don't even include the A/C unit in the dry weight.
So expect trailers in the 28-30' range to be 8-9k loaded... IMHO, 24' is about the realistic limit of that truck.